Interpretability of various extensions of arithmetic
The paper proves some nice theorems about interpretability of extensions of arithmetic PA. The main result: let \(PA_ 0=PA\) and \(PA_{n+1}=PA_ n+Consis PA_ n\), then PA \(+\) arbitrary m examples of the local reflection principle \(\Pr_{PA}(\ulcorner \Phi \urcorner)\to \Phi\) is interpretable in the theory \(PA_ n\) iff \(m\leq n\). It follows immediately that theories \(PA'=PA\) \(+\) local reflection principle and \(PA_{\omega}=\cup_{n\in \omega}PA_ n\) are relatively interpretable. The result seems interesting because \(PA_{\omega}\subset PA'\) and \(PA_{\omega}\) is in the following sense much weaker than PA': \(PA_{\omega}\) is contained in some finite extension of PA and PA' is not.
interpretability of extensions of arithmetic
scientific article; zbMATH DE number 4027458